June/July 2007 noticesoftheAMs 729

years. The general expansion of higher education in India, as well as a migration of talent out of the country, has contributed to a relative scarcity of mathematicians capable of teaching at the level the IITs expect. For this reason, IITB has received official permission to advertise abroad, and hence the advertisements. The difficulties of acquiring enough good faculty in the next few years has also led to consideration of an arrangement of visitor teaching programs.

The Environment of IITBIITB is located in the Mumbai suburb of Powai, a bit to the north east of the city. The campus is fairly self-contained, physically isolated from its neighborhood and relatively attractive. Just to its north lies Sanjay Gandhi National Park, a very large and interesting place to visit—with a couple of large lakes, an ancient temple at Kanheri, and an extremely varied wildlife population. Until a new fence was recently constructed there was a problem on campus with leopards raiding the resident pet population. (This is different in degree but not in kind, I suppose, from the problems with the persistent coyote populations of some North American universities.) There is one large and pleasant lake on the edge of campus, as visitors to the official guest house will recall fondly.

Most faculty as well as staff live on the campus itself; the current plans for expansion include plans for much building construction and renova-tion, of both offices and residences.

ReferencesThe photograph of the Hijli detention center has been taken from the Wikipedia site. http://en.wikipedia.org/wiki/Hijli

Wikipedia also has a good article about the IIT campuses in general:

http://en.wikipedia.org/wiki/Indian_Institutes_of_Technology

The official website for the mathematics depart-ment at IITB is

http://www.math.iitb.ac.in/

A heron in flight over the lake at the western edge of the IITB campus.

About the Cover

Aggregation 22

This month’s cover is from the collection of images http://www.bridgesmathart.org/art-exhibits/bridges06/lomas.html by Andy Lomas, part of the “Bridges London 2006” conference covered by Mike Field elsewhere in this issue. Andy studied mathematics as an undergraduate at Trinity College Cambridge, but is currently head of computer graphics at the English company Framestore CFC, Europe’s largest digital effects and animation studio.

Andy tells us, “Mathematics and visual imagery have played an important role throughout my life. From an early age I have also had deep interests in photography and film-making. Digital art, computer graphics, and animation have provided a very natural and fulfilling way of bringing these two paths together.” As to how the image was constructed, he wrote:

“The structures in the Aggregation series are produced by variations on Diffusion Limited Aggregation (DLA), a sto-chastic model for fractal growth originally proposed by T. L. Witten and L. M. Sander (Physical Review Letters 47).

DLA starts with a seed particle, then deposits new particles onto the structure by creating new ‘walker’ particles and al-lowing them to move randomly by Brownian motion until they reach the aggregated cluster where they are deposited. Iterating this process over many particles, extremely com-plex fractal structures called ‘Brownian Trees’ are formed. Computer implementations of DLA commonly restrict the particles to a lattice grid, but my implementation is lattice-free and calculates the intersections of the walker particles with the clustered form analytically. I have used a piece-wise linear approximation to Brownian motion.

One thing that I find particularly intriguing about Aggrega-tion 22 is that there appear to be distinctly different structures in the form: an interior shape and an outer shell…although there is no point in the simulation where the processes were altered to produce these two structures.

The simulation stage to create the structure of Aggrega-tion 22 took 182 hours on a 3.2 GHz Pentium 4 processor. Rendering the image at a resolution of 8,192 by 8,192 pixels took 28 hours on the same machine.”

“Other examples where I have used mathematics in my professional work include fluid effects for the ‘pool of tears’ sequence in a TV series Alice in Wonderland and an illumina-tion model for rain that allowed us to emulate the effects of rain being illuminated from different angles, to integrate with live action in The Matrix: Revolutions.

Andy’s home page is at www.andylomas.com.

—Bill Casselman, Graphics Editor(notices-covers@ams.org)

* References1. Witten Jr, T. A. and Sander, L. M. , Diffusion-limited aggrega-tion, a kinetic critical phenomenon, Physical Review of Letters 47 (1981), p. 1400.2. Haeckel, E., Kunstformen der Natur, 1904.